Conceptual Synthesis of Compliance at a Single Point

Abstract

In this paper, we investigate a methodology for the conceptual synthesis of compliance at a single point based on a building block approach. The methodology lays the foundation for more general compliant mechanism synthesis problems involving multiple points of interest (i.e. inputs and outputs). In the building block synthesis, the problem specifications are decomposed into related sub-problems if a single building block cannot perform the desired task. The sub-problems are tested against the library of building blocks until a suitable building block is determined. The synthesized design is composed of an assembly of the building blocks to provide the desired functionality. The building block approach is intuitive and provides key insight into how individual building blocks contribute to the overall function. We investigate the basic kinematic behavior of individual building blocks and relate this to the behavior of a design composed of building blocks. This serves to not only generate viable solutions but also to augment the understanding of the designer. Once a feasible concept is thus generated, known methods for size and geometry optimization may be employed to fine tune performance. The key enabler of the building block synthesis is the method of capturing kinematic behavior using Compliance Ellipsoids. The mathematical model of the compliance ellipsoids facilitates the characterization of the building blocks, transformation of problem specifications, decomposition into sub-problems, and the ability to search for alternate solutions. The compliance ellipsoids also give insight into how individual building blocks contribute to the overall kinematic function. The effectiveness and generality of the methodology are demonstrated through a synthesis example. Using only a limited set of building blocks, the methodology is capable of addressing generic kinematic problem specifications.